Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity

• Autorzy: C. Ward Henson , Yves Raynaud
• Języki publikacji: EN

Abstrakty

EN

We give a criterion ensuring that the elementary class of a modular Banach space \(E\) (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of \(E\)) consists of all direct sums \(E\oplus_m H\), where \(H\) is an arbitrary Hilbert space and \(\oplus_m\) denotes the modular direct sum. Also, we give several families of examples in the class of Nakano direct sums of finite dimensional normed spaces that satisfy this criterion. This yields many new examples of uncountably categorical Banach spaces, in the model theory of Banach space structures.

Słowa kluczowe

EN

Banach spaces; ultrapowers; elementary equivalence; isometric embeddings; modular direct sums

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: 56
• Numer: 1

Daty

wydano

2016

online

2016-10-13

Twórcy

autor

C. Ward Henson

autor

Yves Raynaud

Identyfikatory

DOI

10.14708/cm.v56i1.1231